EP3730917B1 - Dispositif de mesure de front d'onde et système de mesure de front d'onde - Google Patents

Dispositif de mesure de front d'onde et système de mesure de front d'onde Download PDF

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Publication number
EP3730917B1
EP3730917B1 EP18901530.8A EP18901530A EP3730917B1 EP 3730917 B1 EP3730917 B1 EP 3730917B1 EP 18901530 A EP18901530 A EP 18901530A EP 3730917 B1 EP3730917 B1 EP 3730917B1
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Prior art keywords
function
pupil
wavefront
unit
point spread
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German (de)
English (en)
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EP3730917A1 (fr
EP3730917A4 (fr
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Masataka Suzuki
Takayuki Yanagisawa
Shigetaka ITAKURA
Takayasu ANADA
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Mitsubishi Electric Corp
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Mitsubishi Electric Corp
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M11/00—Testing of optical apparatus; Testing structures by optical methods not otherwise provided for
    • G01M11/02—Testing optical properties
    • G01M11/0242—Testing optical properties by measuring geometrical properties or aberrations
    • G01M11/0257—Testing optical properties by measuring geometrical properties or aberrations by analyzing the image formed by the object to be tested
    • G01M11/0264—Testing optical properties by measuring geometrical properties or aberrations by analyzing the image formed by the object to be tested by using targets or reference patterns
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M11/00—Testing of optical apparatus; Testing structures by optical methods not otherwise provided for
    • G01M11/02—Testing optical properties
    • G01M11/0242—Testing optical properties by measuring geometrical properties or aberrations
    • G01M11/0257—Testing optical properties by measuring geometrical properties or aberrations by analyzing the image formed by the object to be tested
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M11/00—Testing of optical apparatus; Testing structures by optical methods not otherwise provided for
    • G01M11/005—Testing of reflective surfaces, e.g. mirrors
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
    • G01J9/00—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength
    • G01J2009/002—Wavefront phase distribution
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
    • G01J9/00—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength

Definitions

  • the present invention relates to a technique for measuring a wavefront aberration, and more particularly, to a technique for measuring a wavefront aberration on the basis of a point spread function (PSF).
  • PSF point spread function
  • Wavefront aberration measurement technology is widely used for quantitatively evaluating the characteristics of an object, such as a light source, an optical system (e.g., a lens or a reflector), or a light propagation path (a path through which light propagates between the object and the observation equipment).
  • an optical system e.g., a lens or a reflector
  • a light propagation path a path through which light propagates between the object and the observation equipment.
  • a technique of detecting diffracted light transmitted through the objective lens and measuring a wavefront aberration is known.
  • the optical characteristics of the observation device or the characteristics of the light propagation path may change due to the effects of vibration or the surrounding environment during the operation of the observation device, and thereby wavefront aberrations may be generated.
  • Such a wavefront aberration deteriorates the quality of an observed image. It is possible to use a technique for measuring the wavefront aberration in order to cope with such deterioration of the quality of the observed image. For example, on the basis of the measurement amount of the wavefront aberration, an optical characteristic of the observation device is adaptively corrected, or a change in the characteristic of the light propagation path is compensated so as to reduce the wavefront aberration, and thereby a high-resolution observed image can be obtained.
  • Non-Patent Literatures 1 and 2 There is a plurality of methods for measuring a wavefront aberration.
  • One of these methods is a method of estimating a wavefront aberration on the basis of a point spread function (PSF).
  • PSD point spread function
  • the point spread function theoretically refers to an intensity distribution of a blurred optical image formed on an image plane when an infinitesimal point is imaged.
  • Wavefront aberration estimation techniques based on point spread functions are disclosed in, for example, the following Non-Patent Literatures 1 and 2.
  • Non-Patent Literature 1 discloses a method of estimating a spatial phase distribution of a complex amplitude of light on a pupil plane from an intensity distribution of light observed on an image plane on the basis of an iterative operation algorithm called a Gerchberg-Saxton algorithm (hereinafter, referred to as a "GS algorithm”).
  • the wavefront aberration can be estimated from the estimated spatial phase distribution.
  • Non-Patent Literature 2 discloses a method of detecting a wavefront aberration by using a defocused point spread function on the basis of a modified Gerchberg-Saxton algorithm (hereinafter, referred to as "MGS algorithm").
  • Document JP 2005 331440 A discloses an optical phase distribution measurement method and an optical phase distribution measuring system for measuring optical phase distribution by identifying the optical phase distribution from information on optical intensity distribution which is easily measured, without using special measurement apparatuses.
  • Document JP 2007 534925 A discloses a measuring apparatus for determining data relating to the shape of an input radiation wavefront.
  • the observable wavelength region When the observable wavelength region is wide, influences of light components of various wavelengths are reflected in the point spread function. Specifically, since the size of an Airy disk indicating the minimum spot diameter on the image plane is proportional to the wavelength, different sizes of Airy disk diameter are generated depending on light components of various wavelengths.
  • the spatial phase distribution of the complex amplitude of light on the pupil plane also has wavelength dependency. Therefore, when the observable wavelength region is wide, even if the above-mentioned GS algorithm and MGS algorithm are used, there is a problem that the estimation accuracy of the wavefront aberration degrades due to the wavelength dependency of the Airy disk diameter and the wavelength dependency of the spatial phase distribution on the pupil plane.
  • the wavefront aberration on a pupil plane can be estimated with high precision.
  • FIG. 1 is a block diagram schematically showing a configuration of a wavefront measurement system 1A according to a first embodiment of the present invention.
  • the wavefront measurement system 1A includes a data supply unit 3 that supplies measurement data TD including data of a measured point spread function (PSF) to a wavefront measurement device 2A, and the wavefront measurement device 2A that measures a wavefront aberration on a pupil plane of an optical system on the basis of point spread function data included in the measurement data TD.
  • the data supply unit 3 and the wavefront measurement device 2A are connected via a wired communication path such as a cable or a wireless communication path.
  • the data supply unit 3 has a communication function of transferring measured point spread function data to the wavefront measurement device 2A.
  • the data supply unit 3 may further have a function as a detector that detects a point image and generates a point spread function.
  • FIG. 2 is a diagram schematically showing an example of arrangement of a pupil plane and an image plane of the optical system.
  • the point spread function refers to an intensity distribution of a blurred optical image (an optical image having a spatial spread) observed on an image plane when the optical system images a point light source.
  • the pupil plane and the image plane are separated from each other in the z-axis direction.
  • the spatial coordinates of the rectangular coordinate system on the pupil plane are represented by ( ⁇ , ⁇ )
  • the spatial coordinates of the rectangular coordinate system on the image plane are represented by (x, y).
  • the wavefront measurement device 2A of the present embodiment includes a wavefront setting unit 10, a first pupil-function generating unit 11, a first image-plane amplitude calculating unit 12, a constraint condition applying unit 13, a third pupil-function generating unit 14, a wavefront calculation unit 15, a data output unit 16, a second pupil-function generating unit 21, a second image-plane amplitude calculating unit 22, a PSF correction unit 23, and a data reception unit 30.
  • the data reception unit 30 receives the measurement data TD transferred from the data supply unit 3 and supplies data of a point spread function PS M included in the measurement data TD to the PSF correction unit 23.
  • the wavefront measurement device 2A can calculate the wavefront aberration on the pupil plane by executing an iterative operation using the point spread function PS M .
  • the wavefront setting unit 10 sets an initial wavefront aberration W 0 for the iterative operation and supplies the set initial wavefront aberration W 0 to the first pupil-function generating unit 11 and the second pupil-function generating unit 21.
  • the initial wavefront aberration W 0 can be set to have an arbitrary wavefront shape.
  • the wavefront setting unit 10 can set the initial wavefront aberration W 0 in a format of image data or a format that specifies Zernike coefficients.
  • the initial wavefront aberration W 0 is expressed by the following equation (1).
  • W 0 ( ⁇ , ⁇ ) is a function representing the initial wavefront aberration W 0 on the pupil plane
  • ⁇ , ⁇ is the value of the spatial coordinates of the rectangular coordinate system on the pupil plane
  • z k is the k-th Zernike Coefficients
  • Ck is the k-th Zernike Terms
  • K is a positive integer indicating the number of modes.
  • the Zernike terms C k ( ⁇ , ⁇ ) is known.
  • the first pupil-function generating unit 11 calculates a first optical phase distribution on the pupil plane at a reference wavelength ⁇ 0 .
  • the first pupil-function generating unit 11 generates a first pupil function G 0 representing a complex amplitude distribution on the pupil plane by applying a first constraint condition (pupil plane constraint condition) to the first optical phase distribution, and supplies the generated first pupil function G 0 to the first image-plane amplitude calculating unit 12.
  • the reference wavelength ⁇ 0 is a reference wavelength selected from an observable wavelength region (hereinafter, referred to as "multi-wavelength region”) including various wavelengths.
  • the first optical phase distribution O( ⁇ , ⁇ , ⁇ ) for the wavelength ⁇ is represented by the following equation (2).
  • O ⁇ ⁇ ⁇ exp 2 ⁇ i W ⁇ ⁇ ⁇
  • ⁇ is an arbitrary wavelength in a multi-wavelength region
  • W( ⁇ , ⁇ ) is a function representing a wavefront aberration on a pupil plane
  • O( ⁇ , ⁇ , ⁇ ) is a function representing the complex amplitude distribution of light on the pupil plane for the wavelength ⁇
  • the first pupil function G 0 ( ⁇ , ⁇ ) is expressed by, for example, the following equation (4).
  • t( ⁇ , ⁇ ) is a function that determines a first constraint condition applied to the first optical phase distribution O( ⁇ , ⁇ , ⁇ 0 )
  • W( ⁇ , ⁇ ) is W 0 ( ⁇ , ⁇ ) or W 1 ( ⁇ , ⁇ ).
  • t( ⁇ , ⁇ ) spatially limits the intensity on the pupil plane.
  • t( ⁇ , ⁇ ) is set so that the intensity of the pupil function is constant inside the circular opening APT of the pupil plane and is zero outside the circular opening.
  • t( ⁇ , ⁇ ) can be expressed by the following equation (5).
  • I 0 is a constant value
  • D is a diameter of the circular opening APT.
  • the first image-plane amplitude calculating unit 12 calculates a first image plane amplitude A 0 representing the complex amplitude distribution on the image plane at the reference wavelength ⁇ 0 , and gives the calculated first image plane amplitude A 0 to the constraint condition applying unit 13 and the PSF correction unit 23.
  • the first image-plane amplitude calculating unit 12 can calculate the first image plane amplitude A 0 by using parameters such as an F value of the optical system and a wavelength sensitivity of the observation system.
  • a 0 (x, y) is a function representing the complex amplitude distribution on the image plane.
  • x and y are variables corresponding to ⁇ and ⁇ , respectively, and are values of the spatial coordinates of the rectangular coordinate system on the image plane.
  • f represents the focal length of an imaging system.
  • the second pupil-function generating unit 21 calculates the second optical phase distribution on the pupil plane at the multi-wavelength region.
  • the second pupil-function generating unit 21 generates a second pupil function G 1 representing the complex amplitude distribution on the pupil plane by applying the first constraint condition to the second optical phase distribution, and supplies the generated second pupil function G 1 to the second image-plane amplitude calculating unit 22.
  • the second image-plane amplitude calculating unit 22 calculates a second image plane amplitude A 1 representing a complex amplitude distribution on an image plane at a multi-wavelength region on the basis of the second pupil function G 1 , and gives the calculated second image plane amplitude A 1 to the PSF correction unit 23.
  • the second image-plane amplitude calculating unit 22 can calculate the second image plane amplitude A 1 by using parameters such as the F value of the optical system and the wavelength sensitivity of the observation system.
  • the second pupil function G 1 is expressed by using the above equation (2) as shown in the following equation (7).
  • G 1 ( ⁇ ⁇ ) is a function representing the second pupil function on the pupil plane.
  • the second pupil function G 1 ( ⁇ , ⁇ ) includes components of various wavelengths at a multi-wavelength region. Therefore, when the lower limit (minimum wavelength) of the multi-wavelength region is represented by ⁇ 1 , and the upper limit (maximum wavelength) of the multi-wavelength region is represented by ⁇ 2 , the second image plane amplitude A 1 can be calculated by integrating the complex amplitude distribution on the image plane at the multi-wavelength region.
  • the second image plane amplitude A 1 is expressed, for example, by the following equation (8).
  • a 1 (x, y) is a function of the second image plane amplitude representing the complex amplitude distribution on the image plane.
  • the PSF correction unit 23 receives the point spread function PS M supplied from the data reception unit 30 as an input.
  • the point spread function PS M is a measured light intensity distribution and reflects influences of various wavelengths in a multi-wavelength region that is an observable wavelength region. For this reason, if the wavefront aberration is calculated using the point spread function PS M as it is, the estimation accuracy of the wavefront aberration may be degraded. Therefore, the PSF correction unit 23 of the present embodiment uses the spatial frequency component of the first image plane amplitude A 0 and the spatial frequency component of the second image plane amplitude A 0 to suppress the spatial frequency components at wavelengths other than the reference wavelength ⁇ 0 in the spatial frequency components of the point spread function PS M , thereby correcting the point spread function PS M .
  • the PSF correction unit 23 gives a corrected point spread function PSs (hereinafter, referred to as "corrected point spread function PSs”) to the constraint condition applying unit 13.
  • the PSF correction unit 23 has a coefficient calculation unit 24 that calculates a ratio of a spatial frequency component of the first image plane amplitude A 0 to a spatial frequency component of the second image plane amplitude A 1 as a correction coefficient H, and a PSF generation unit 25 that executes a Fourier transform of the point spread function PS M to calculate a transfer function indicating a spatial frequency component.
  • the PSF generation unit 25 calculates a weighted transfer function by weighting the transfer function with the correction coefficient H, and generates a corrected point spread function PSs by executing an inverse Fourier transform of the weighted transfer function.
  • the intensity distribution D 0 (x, y) of the first image plane amplitude A 0 (x, y) is given by the product of the first image plane amplitude A 0 (x, y) and its complex conjugate A 0 ⁇ (x, y)
  • the intensity distribution D 1 (x, y) of the second image plane amplitude A 1 (x, y) is given by the product of the second image plane amplitude A 1 (x, y) and its complex conjugate A1 ⁇ (x, y).
  • a transfer function T 0 (u, v) representing a spatial frequency component of the first image plane amplitude A 0 can be expressed by the following equation (9).
  • T 0 u v F 1 D 0 x y
  • u and v are variables respectively corresponding to x and y, and are values of coordinates in a rectangular coordinate system on a spatial frequency domain.
  • a transfer function T 1 (u, v) representing a spatial frequency component of the second image plane amplitude A 1 can be expressed by the following equation (10).
  • T 1 u v F 1 D 1 x y
  • the correction coefficient H can be expressed, for example, by the following equation (11).
  • H u v T 0 u v / T 1 u v
  • H(u, v) is a function representing a correction coefficient in the spatial frequency domain.
  • the correction coefficient H(u, v) shown in the equation (11) is a ratio between a transfer function T 1 (u, v) representing a spatial frequency component of the second image plane amplitude A 1 and a transfer function T 0 (u, v) representing a spatial frequency component of the first image plane amplitude A 0, that is, a ratio between a transfer function T 1 (u, v) representing a spatial frequency spectrum component of the intensity distribution D 1 (x, y) at a multi-wavelength region (wavelength band from ⁇ 1 to ⁇ 2 ) and a transfer function T 0 (u, v) representing a spatial frequency spectrum component of the intensity distribution D 0 (x, y) at the reference wavelength ⁇ 0 .
  • the intensity distribution D 1 (x, y) at the multi-wavelength region is a distribution in which a plurality of intensity distributions at a plurality of wavelengths in the multi-wavelength region is superimposed.
  • the measured point spread function is an intensity distribution function obtained by superimposing a plurality of point spread functions at a plurality of wavelengths in the multi-wavelength region.
  • the coefficient calculation unit 24 can calculate the correction coefficient H(u, v) according to the above equation (11).
  • the PSF generation unit 25 calculates a transfer function PT M (u, v) indicating a spatial frequency component by executing a two-dimensional Fourier transform of the point spread function PS M (x, y) as shown in the following equation (12).
  • PT M u v F 1 PS M x y
  • the PSF generation unit 25 calculates a weighted transfer function PTs(u, v) by weighting the transfer function PT M (u, v) with the correction coefficient H(u, v) as shown in the following equation (13).
  • PT s u v H u v ⁇ PT M u v
  • the PSF generation unit 25 can calculate the corrected point spread function PSs(x, y) by executing an inverse Fourier transform of the weighted transfer function PTs(u, v) as shown in the following equation (14).
  • PS s x y F 1 ⁇ 1 PT s u v
  • F1 -1 [] is an inverse transform operator for the two-dimensional Fourier transform operator F1[].
  • the correction coefficient (u, v) forms a distribution that relatively reduces the spatial frequency components of wavelengths other than the reference wavelength ⁇ 0 and relatively emphasizes the spatial frequency component of the reference wavelength ⁇ 0
  • the corrected point spread function PSs(x, y) spatial frequency components at wavelengths other than the reference wavelength ⁇ 0 are relatively suppressed, and the spatial frequency component at the reference wavelength ⁇ 0 is relatively emphasized. Therefore, the influence of chromatic aberration on the measured point spread function PS M is corrected.
  • the constraint condition applying unit 13 receives the first image plane amplitude A 0 and the corrected point spread function PSs as inputs and applies a second constraint condition (image plane constraint condition) using the corrected point spread function PSs to a first image plane amplitude A 0 to correct the first image plane amplitude A 0 , thereby calculating a third image plane amplitude A 2 .
  • the constraint condition applying unit 13 calculates the third image plane amplitude A 2 by replacing the real part (actual amplitude) of the first image plane amplitude A 0 with the real part (actual amplitude) of the image plane amplitude (complex amplitude) corresponding to the corrected point spread function PSs.
  • the third image plane amplitude A 2 is expressed by the following equation (16).
  • a 2 (x, y) is a function of the third image plane amplitude A 2 representing the complex amplitude distribution on the image plane.
  • the third pupil-function generating unit 14 generates a third pupil function G 2 on the basis of the third image plane amplitude A 2 .
  • the third pupil-function generating unit 14 generates the third pupil function G 2 on the basis of the following equation (17).
  • G 2 ⁇ ⁇ ⁇ 0 f ⁇ F 0 ⁇ 1 A 2 x y
  • G 2 ( ⁇ , ⁇ ) is a function of the third pupil function G 2 representing a complex amplitude distribution on a pupil plane
  • F 0 -1 [] is an inverse transform operator for a two-dimensional Fourier transform operator F 0 [].
  • W 1 ( ⁇ , ⁇ ) is a function representing the wavefront aberration W 1 on the pupil plane
  • arg[x] is a phase component of an arbitrary complex number x.
  • the wavefront calculation unit 15 can cause the first pupil-function generating unit 11 and the second pupil-function generating unit 21 to execute an iterative operation by feeding back and inputting the calculated data of the wavefront aberration W 1 to the first pupil-function generating unit 11 and the second pupil-function generating unit 21.
  • the first pupil-function generating unit 11, the first image-plane amplitude calculating unit 12, the second pupil-function generating unit 21, the second image-plane amplitude calculating unit 22, the PSF correction unit 23, the constraint condition applying unit 13, the third pupil-function generating unit 14, and the wavefront calculation unit 15 execute an iterative operation until the calculated wavefront aberration W 1 satisfies a convergence condition.
  • the convergence condition may be, for example, a condition that an iterative operation is executed a prespecified number of times.
  • the data output unit 16 When the wavefront aberration W 1 satisfies the convergence condition, the data output unit 16 outputs wavefront data WD indicating the wavefront aberration W 1 to the outside of the data output unit 16.
  • the wavefront data WD may be displayed on a display device (not shown) in the form of image data or in the form specifying Zernike coefficients, or may be stored in a memory. Further, the wavefront data WD may be supplied to a wavefront control device (not shown) forming a part of an adaptive optics system.
  • the wavefront control device is a device that corrects the shape of the incident light wavefront on the basis of the wavefront data WD.
  • the hardware configuration of the above-described wavefront measurement device 2A may include, for example, one or more processors having a semiconductor integrated circuit such as a digital signal processor (DSP), an application specific integrated circuit (ASIC) or a field-programmable gate array (FPGA).
  • the hardware configuration of the wavefront measurement device 2A may include one or more processors including an arithmetic device such as a central processing unit (CPU) or a graphics processing unit (GPU) that executes program code of software or firmware read from a non-volatile memory.
  • the hardware configuration of the wavefront measurement device 2A may include one or more processors including a combination of a semiconductor integrated circuit such as a DSP and an arithmetic device such as a CPU.
  • FIG. 2 is a block diagram schematically showing a configuration of an information processing device 40 that is an example of a hardware configuration that achieves the function of the wavefront measurement device 2A.
  • the information processing device 40 includes a processor 41, a memory 42, an input interface unit 43, an output interface unit 44, and a signal path 45.
  • the signal path 45 is a bus for mutually connecting the processor 41, the memory 42, the input interface unit 43, and the output interface unit 44.
  • the input interface unit 43 has a function of transferring measurement data TD input from the outside to the processor 41 via the signal path 45.
  • the processor 41 generates wavefront data WD by using the transferred measurement data TD, and can output the wavefront data WD to an external device such as a wavefront control device or a data storage device via the signal path 45 and the output interface unit 44.
  • the memory 42 is a data storage area used when the processor 41 executes digital signal processing.
  • the memory 42 has a data storage area for storing a program code of software or firmware executed by the processor 41.
  • a memory 42 for example, a semiconductor memory such as a read only memory (ROM) and a synchronous dynamic random access memory (SDRAM) can be used.
  • FIG. 3 is a flowchart schematically showing an example of the procedure of wavefront measurement processing according to the first embodiment.
  • the wavefront setting unit 10 sets an initial wavefront aberration W 0 , and supplies the set initial wavefront aberration W 0 to the first pupil-function generating unit 11 and the second pupil-function generating unit 21 (step ST11).
  • the first pupil-function generating unit 11 calculates the first optical phase distribution on the pupil plane at the reference wavelength ⁇ 0 on the basis of the input data of the initial wavefront aberration W 0 , and generates the first pupil function G 0 by applying the first constraint condition (pupil plane constraint condition) to the first optical phase distribution (step ST12).
  • the first image-plane amplitude calculating unit 12 calculates the first image plane amplitude A 0 at the reference wavelength ⁇ 0 on the basis of the first pupil function G 0 (step ST13).
  • the second pupil-function generating unit 21 calculates the second optical phase distribution on the pupil plane at a multi-wavelength region on the basis of the input data of the initial wavefront aberration W 0 , and generates the second pupil function G 1 by applying the first constraint condition to the second optical phase distribution (step ST14).
  • the second image-plane amplitude calculating unit 22 calculates the second image plane amplitude A 1 at a multi-wavelength region on the basis of the second pupil function G 1 (step ST15). Note that, steps ST12 and ST13 and steps ST14 and ST16 may be executed in the reverse order of the above processing order, or may be executed simultaneously and in parallel.
  • the coefficient calculation unit 24 calculates, as the correction coefficient H, the ratio of the spatial frequency component of the first image plane amplitude A 0 to the spatial frequency component of the second image plane amplitude A 1 (step ST16).
  • the PSF generation unit 25 acquires the measured point spread function (measured PSF) PS M from the data reception unit 30 (step ST17), and calculates the corrected point spread function (corrected PSF) PSs by correcting the point spread function PS M by using the correction coefficient H (step ST18).
  • the constraint condition applying unit 13 applies the second constraint condition (image plane constraint condition) using the corrected point spread function PSs to the first image plane amplitude A 0 to correct the first image plane amplitude A 0 , thereby calculating the third image plane amplitude A 2 (step ST19).
  • the third pupil-function generating unit 14 generates the third pupil function G 2 on the basis of the third image plane amplitude A 2 (step ST20).
  • the wavefront calculation unit 15 calculates the wavefront aberration W 1 on the pupil plane on the basis of the third pupil function G 2 (step ST21).
  • the wavefront calculation unit 15 determines whether or not to end the wavefront measurement processing (step ST22). Specifically, when the wavefront aberration W 1 does not satisfy the convergence condition described above, the wavefront calculation unit 15 does not end the wavefront measurement processing (NO in step ST22) and causes the first pupil-function generating unit 11 and the second pupil-function generating unit 21 to execute the iterative operation by feeding back and inputting the calculated data of the wavefront aberration W 1 to the first pupil-function generating unit 11 and the second pupil-function generating unit 21 (steps ST12 to ST21). Thereafter, when the wavefront aberration W 1 satisfies the convergence condition described above, the wavefront calculation unit 15 determines to end the wavefront measurement processing (YES in step ST22). In this case, the data output unit 16 outputs the wavefront data WD indicating the wavefront aberration W 1 to the outside of the data output unit 16 (step ST23).
  • the wavefront measurement device 2A executes iterative processing by using the corrected point spread function PSs generated by the PSF correction unit 23 instead of using the measured point spread function PS M as it is.
  • the corrected point spread function PSs spatial frequency components at wavelengths other than the reference wavelength ⁇ 0 are relatively suppressed, and a spatial frequency component at the reference wavelength ⁇ 0 is relatively emphasized. Therefore, the wavefront measurement device 2A can accurately estimate the wavefront aberration W 1 on the pupil plane even when the observable wavelength region, that is, the multi-wavelength region is wide.
  • a detector such as an imaging device has sensitivity to light at a multi-wavelength region of a finite width, and as the bandwidth of the multi-wavelength region is wider with respect to its center wavelength, the difference in the observed image between the wavelengths increases due to the wavelength dependency of the Airy disk diameter of the observed diffraction image and the wavelength dependency of the spatial phase on the pupil plane caused by the wavefront aberration. For this reason, if the wavefront aberration is calculated using the point spread function PS M as it is, the estimation accuracy of the wavefront aberration may be degraded. On the other hand, in the present embodiment, since the wavefront aberration is calculated using the corrected point spread function PSs(x, y), the wavefront aberration W 1 can be estimated with high accuracy.
  • the wavefront measurement device 2A executes the iterative operation until the calculated wavefront aberration W 1 satisfies the convergence condition, the corrected point spread function PSs approaches an ideal distribution in the process of the iterative operation. Therefore, a synergistic effect that the estimation accuracy of the corrected point spread function PSs is improved and the estimation accuracy of the wavefront aberration W 1 is improved at the same time can be expected.
  • FIG. 5 is a block diagram schematically showing a configuration of a wavefront measurement system 1B according to the second embodiment of the present invention.
  • the wavefront measurement system 1B includes a detector 4 that supplies detection data DD indicating a plurality of point spread functions, and a wavefront measurement device 2B.
  • the configuration of the wavefront measurement device 2B is the same as the configuration of the wavefront measurement device 2A of the first embodiment except that the data reception unit 30 in FIG. 1 is replaced with a PSF reconstruction unit 31 in FIG. 5 .
  • the detector 4 has a function of imaging a plurality of point light sources (targets) for evaluating a point spread function (PSF) and detecting a plurality of point spread functions.
  • the detector 4 may be composed of, for example, a high-sensitivity imaging device.
  • FIG. 6 is a diagram showing how the detector 4 images three targets Tg, Tg, and Tg.
  • FIG. 7 is a schematic diagram showing point image distributions Pa, Pb, and Pc detected on the basis of observed images of these three targets Tg, Tg, and Tg.
  • the detector 4 transfers the detection data DD indicating the plurality of detected point spread functions to the wavefront measurement device 2B.
  • the target for PSF evaluation may be, for example, a light source installed on the ground as described in Non-Patent Literature 3 below, or a star as described in Non-Patent Literature 4 below.
  • Non-Patent Literature 3 M. Taylor, “In-flight performance assessment of imaging systems using the specular array radiometric calibration (SPARC) method", 11th Annual Joint Agency Commercial Imagery Evaluation (JACIE) Workshop (2012 ).
  • Non-Patent Literature 4 Jay Anderson and Ivan R. King, "Toward High-Precision Astrometry with WFPC2.I. Deriving an Accurate Point-Spread Function", PASP, Vol. 112, No. 776, pp. 1360-1382, (2000 ).
  • the PSF reconstruction unit 31 reconstructs a single point spread function on the basis of a plurality of point spread functions included in the detection data DD, and can supply the single point spread function to the PSF correction unit 23 as a measured point spread function PS M .
  • the PSF reconstruction unit 31 calculates a spatial phase of a plurality of point spread functions and can reconstruct a high-resolution point spread function PS M by combining the plurality of point spread functions on the basis of the calculation results.
  • the detector 4 detects a plurality of point images each having a size less than the detector pitch and having a different phase shift, and thereby the PSF reconstruction unit 31 can reconstruct a higher-resolution point spread function.
  • the point image distribution Pa is formed at the center of the detector 4, and the point image distributions Pb and Pc are formed at positions shifted rightward with respect to the point image distribution Pa.
  • the PSF reconstruction unit 31 can reconstruct a high-resolution point spread function PS M by combining the point spread functions of these point image distributions Pa, Pb, and Pc.
  • the above-described phase shift of less than the detector pitch can be made to occur.
  • the spatial resolution of the imaging device is d meters, for example, if a plurality of light sources is arranged at regular intervals with an interval of 1.2 ⁇ d meters, on a captured image obtained by imaging the plurality of light sources, it is possible to set conditions so that a plurality of point images arranged at equal intervals at 0.2 pixel intervals appears.
  • an adjacent second point image has a phase shift of 0.2 pixels less than the detector pitch.
  • a third point image adjacent to the second point image has a phase shift of 0.4 pixels with respect to the first point image.
  • FIG. 8 is a schematic diagram for explaining an example of a method of reconstructing a point spread function.
  • each point spread function Pk (k is an arbitrary integer of 1 to N-1) is assumed to include a pixel value sequence ⁇ Pk(0), P k (1),..., P k (M-1) ⁇ (M is a positive integer) composed of M pixel values.
  • the PSF reconstruction unit 31 rearranges the pixel values of the point spread functions P 0 , P 1 ,..., P N-1 to generate a pixel value sequence having an arrangement as shown below, thereby obtaining a point spread function P r having ⁇ times higher resolution.
  • it is desirable that the obtained high-resolution point spread function P r is normalized so that the sum of the pixel values is one.
  • FIG. 8 illustrates a method of reconstructing a one-dimensional point spread function
  • a two-dimensional point spread function may be reconstructed by applying a similar method.
  • the wavefront measurement device 2B executes iterative processing using the corrected point spread function PSs generated by the PSF correction unit 23 instead of using the measured point spread function PS M as it is, it is possible to estimate the wavefront aberration W 1 on the pupil plane with high accuracy even if the observable wavelength region, that is, the multi-wavelength region is wide.
  • the PSF reconstruction unit 31 reconstructs the high-resolution point spread function PS M on the basis of the plurality of point spread functions, compared with the case of the first embodiment, the wavefront aberration W 1 can be estimated with higher accuracy.
  • FIG. 9 is a block diagram schematically showing a configuration of a wavefront measurement system 1C according to the third embodiment of the present invention.
  • the wavefront measurement system 1C includes a wavefront control device 5 that corrects the distortion of an incident light wavefront IW and outputs a light wavefront CW, an observation device 6 that observes the light wavefront CW, a detector 4A that detects an image of the light wavefront CW and outputs the detection data DD, and the wavefront measurement device 2B ( FIG. 5 ) that outputs wavefront data WD on the basis of the detection data DD.
  • the detector 4A has a function of imaging a plurality of point light sources (targets) for evaluating a point spread function (PSF) and detecting one or more point spread functions.
  • the detector 4 may be composed of, for example, a high-sensitivity imaging device.
  • the detector 4 transfers the detection data DD indicating one or more detected point spread functions to the wavefront measurement device 2B.
  • the wavefront measurement device 2B may execute the wavefront measurement processing by using the single point spread function.
  • the wavefront measurement device 2B estimates the wavefront aberration W 1 on the basis of the detection data DD and outputs the wavefront data WD indicating the estimated wavefront aberration W 1 to the wavefront control device 5.
  • the wavefront control device 5 can correct the distortion of the light wavefront IW incident from the external space on the basis of the wavefront data WD. Therefore, since the wavefront control device 5 can correct the wavefront aberration caused by the change in the characteristic of the light propagation path (for example, fluctuation of the atmosphere), the observation device 6 can obtain a high-resolution observed image. Therefore, the wavefront measurement system 1C constitutes an adaptive optics system.
  • the wavefront control device 5 may have a configuration to correct the distortion of the incident light wavefront IW, for example, by using a deformable mirror, as described in Non-Patent Literature 5 below, or, as described in Non-Patent Literature 6 below, may have a configuration to correct the distortion of the incident light wavefront IW by adjusting the optical characteristics of the diffractive optical system.
  • Non-Patent Literature 5 Mingshuang Huang, Zhizheng Wu, Lingkun Min, Junqiu Wu, "Adaptive Surface Shape Control for Magnetic Fluid Deformable Mirrors", International Conference on Control, Automation and Information Sciences (ICCAIS) (2015 ).
  • Non-Patent Literature 6 Li Dongming, Gai Mengye, Chen Haochuan, Zhu Guang, and Zhang Lijuan, "Research on Wavefront Correction Algorithm of Adaptive Optics System", 4th International Conference on Computer Science and Network Technology (ICCSNT) (2015 ).
  • FIG. 10 is a block diagram schematically showing a configuration example of the wavefront control device 5.
  • the wavefront control device 5 includes a wavefront control element 51 having a deformable reflection surface and an element control unit 54 for controlling the operation of the wavefront control element 51.
  • the wavefront control element 51 includes micromirrors 52,..., 52 for reflecting the incident light wavefront IW to form an output light wavefront CW, and an actuator (drive unit) 53 for adjusting the direction of the reflection surface of each of these micromirrors 52,..., 52.
  • Most of the output light wavefront CW enters the observation device 6 via a beam splitter 7.
  • the element control unit 54 controls the actuator 53 on the basis of the wavefront data WD to adjust the shape of the reflection surface of the entire micromirrors 52,..., 52, thereby allowing the wavefront control element 51 to correct the distortion of the light wavefront IW incident from the external space.
  • FIG. 11 is a block diagram schematically showing a configuration of a wavefront measurement system ID according to the fourth embodiment of the present invention.
  • the wavefront measurement system ID includes a wavefront control device 5 that corrects the shape of the incident light wavefront IW and outputs the light wavefront CW, a detector 4B incorporated in the observation device 6 that observes the output light wavefront CW and the wavefront measurement device 2B ( FIG. 5 ) that outputs wavefront data WD on the basis of the detection data DD supplied from the detector 4B.
  • the detector 4B is an observation detector including a high-sensitivity imaging device.
  • the detector 4B has a function of imaging a plurality of point light sources (targets) for evaluating a point spread function (PSF) and detecting one or more point spread functions.
  • the detector 4B transfers the detection data DD indicating one or more detected point spread functions to the wavefront measurement device 2B.
  • the wavefront measurement device 2B may execute the wavefront measurement processing by using the single point spread function.
  • the wavefront measurement device 2B estimates the wavefront aberration W 1 on the basis of the detection data DD and outputs the wavefront data WD indicating the estimated wavefront aberration W 1 to the wavefront control device 5.
  • the wavefront control device 5 has a function of correcting the shape of the light wavefront IW incident from the external space on the basis of the wavefront data WD.
  • the wavefront measurement device 2B can estimate the wavefront aberration W 1 caused by a change in the characteristics of the optical system (the imaging optical system or the reflection optical system or both of them) (for wavefront aberration W 1 caused by a change in the characteristics of the optical system (the imaging optical system or the reflection optical system or both of them) (for example, a change in the optical characteristics due to a temperature change) inside the observation device 6. Since the wavefront control device 5 can compensate for characteristics such as the imaging performance of the optical system inside the observation device 6, the observation device 6 can obtain a high-resolution observed image. Therefore, the wavefront measurement system ID constitutes an adaptive optics system.
  • the hardware configuration of the wavefront measurement device 2B of the second embodiment may include, as in the case of the first embodiment, for example, one or more processors having a semiconductor integrated circuit such as a DSP, an ASIC, or an FPGA.
  • the hardware configuration of the wavefront measurement device 2B may include one or more processors including an arithmetic device such as a CPU or a GPU that executes a program code of software or firmware read from a memory.
  • the hardware configuration of the wavefront measurement device 2B may include one or more processors including a combination of a semiconductor integrated circuit such as a DSP and an arithmetic device such as a CPU.
  • the hardware configuration of the wavefront measurement device 2B may include the information processing device 40 shown in FIG. 3 .
  • the wavefront measurement device and the wavefront measurement system according to the present invention can be used to measure or evaluate characteristics of an object such as a light source, an optical system (e.g., a lens or a reflector) or a light propagation path, and, for example, it can be used in an adaptive optics system, or a system that inspects characteristics of a light source or an optical system.
  • an optical system e.g., a lens or a reflector
  • a light propagation path e.g., a light propagation path
  • an adaptive optics system e.g., a system that inspects characteristics of a light source or an optical system.
  • 1A, 1B, 1C, and 1D Wavefront measurement system
  • 2A and 2B Wavefront measurement device
  • 3 Data supply unit
  • 4, 4A, and 4B Detector
  • 5 Wavefront control device
  • 6 Observation device
  • 7 Beam splitter
  • 10 Wavefront setting unit
  • 11 First pupil-function generating unit
  • 12 First image-plane amplitude calculating unit
  • 13 Constraint condition applying unit
  • 14 Third pupil-function generating unit
  • 16 Data output unit
  • 22 Second image-plane amplitude calculating unit
  • 23 PSF correction unit
  • 24 Coefficient calculation unit
  • 30 Data reception unit
  • 40 Information processing device
  • 41: Processor 42: Memory
  • 43 Input interface unit
  • 44 Output interface unit
  • 45 Signal path
  • 51 Wavefront control element
  • 52 Micromirror
  • 53 Actuator
  • 54 Element control unit.

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Claims (8)

  1. Dispositif de calcul de front d'onde comprenant :
    une première unité de génération de fonction pupillaire (11) pour générer une première fonction pupillaire en calculant une première distribution de phase optique sur un plan pupillaire à une longueur d'onde de référence sélectionnée dans une région de longueurs d'onde multiples sur la base de données d'entrée d'une aberration de front d'onde et en appliquant une première condition de contrainte à la première distribution de phase optique, dans lequel la première distribution de phase optique est représentée par l'équation O ξ η λ = exp 2 π i W ξ η λ
    Figure imgb0043
    où 0(ξ, η, λ) est la première distribution de phase optique, λ est une longueur d'onde arbitraire dans une région de longueurs d'onde multiples, W(ξ, η) est une fonction représentant une aberration de front d'onde sur le plan pupillaire, ξ et η sont des coordonnées spatiales d'un système de coordonnées rectangulaires sur le plan pupillaire, et i est une unité imaginaire, et dans lequel la première fonction de pupille est exprimée par l'équation G 0 ξ η = t ξ η × O ξ η λ 0 = t ξ η × exp 2 π i W ξ η λ 0
    Figure imgb0044
    où G0(ξ, η) est la première fonction pupillaire, la fonction t(ξ, η) est réglée de telle sorte qu'une intensité de la fonction pupillaire est constante à l'intérieur d'une ouverture circulaire du plan pupillaire et est nulle à l'extérieur de l'ouverture circulaire, et λ 0 est une longueur d'onde de référence choisie dans une région de longueurs d'onde observables ; et
    une première unité de calcul d'amplitude de plan d'image (12) pour calculer une première amplitude de plan d'image à la longueur d'onde de référence sur la base de la première fonction pupillaire, dans laquelle la première amplitude de plan d'image est exprimée par l'équation A 0 x y = 1 λ 0 f F 0 G 0 ξ η = 1 λ 0 f F 0 t ξ η × exp 2 π i W ξ η λ 0
    Figure imgb0045
    où A0(x, y) est la première amplitude de plan d'image, F0[] représente un opérateur de transformée de Fourier bidimensionnelle du plan pupillaire au plan d'image, x et y sont des variables correspondant à ξ et η, respectivement, et sont des valeurs des coordonnées spatiales d'un système de coordonnées rectangulaires sur le plan d'image, et f représente la distance focale d'un système d'imagerie ;
    caractérisé en ce que le dispositif de calcul de front d'onde comprend en outre :
    une deuxième unité de génération de fonction pupillaire (21) pour générer une deuxième fonction pupillaire en calculant une seconde distribution de phase optique sur le plan pupillaire dans la région de longueurs d'onde multiples sur la base des données d'entrée et en appliquant la première condition de contrainte à la seconde distribution de phase optique, dans lequel la deuxième fonction pupillaire est exprimée comme indiqué dans l'équation G 1 ξ η = t ξ η × O ξ η λ = t ξ η × exp 2 π i W ξ η λ
    Figure imgb0046
    où G1 (ξ, η) est la deuxième fonction pupillaire ;
    une seconde unité de calcul d'amplitude de plan d'image (22) pour calculer une seconde amplitude de plan d'image dans la région de longueurs d'onde multiples sur la base de la deuxième fonction pupillaire, dans lequel la seconde amplitude de plan d'image est exprimée par l'équation A 1 x y = ∫ λ 1 λ 2 d λ 1 λ f F 0 G 1 ξ η = ∫ λ 1 λ 2 d λ 1 λ f F 0 t ξ η × exp 2 π i W ξ η λ
    Figure imgb0047
    où A1 est la seconde amplitude de plan d'image, λ 1 est la limite inférieure de la région de longueurs d'onde multiples, et λ 2 est la limite supérieure de la région de longueurs d'onde multiples ;
    une unité de correction PSF (23) pour corriger une fonction d'étalement de point mesurée en supprimant les composantes de fréquence spatiale à des longueurs d'onde autres que la longueur d'onde de référence dans les composantes de fréquence spatiale de la fonction d'étalement de point en utilisant une composante de fréquence spatiale de la première amplitude de plan d'image et une composante de fréquence spatiale de la seconde amplitude de plan d'image, dans lequel l'unité de correction PSF (23) comprend une unité de calcul de coefficient (24) pour calculer un rapport de la composante de fréquence spatiale de la première amplitude de plan d'image sur la composante de fréquence spatiale de la seconde amplitude de plan d'image en tant que coefficient de correction, et une unité de génération de PSF (25) pour calculer une fonction de transfert en exécutant une transformation de Fourier de la fonction d'étalement de point mesurée et en calculant une fonction de transfert pondérée en pondérant la fonction de transfert avec le coefficient de correction, et l'unité de génération de PSF (25) génère la fonction d'étalement de point corrigée en exécutant une transformation de Fourier inverse de la fonction de transfert pondérée ;
    une unité d'application de condition de contrainte (13) destinée à appliquer une seconde condition de contrainte en utilisant la fonction d'étalement de point corrigée à la première amplitude de plan d'image pour corriger la première amplitude de plan d'image, dans lequel la première amplitude de plan d'image corrigée est exprimée par l'équation A 2 x y = A 0 x y A s x y A 0 x y = A 0 x y PS s x y A 0 x y
    Figure imgb0048
    où A2(x, y) est la première amplitude de plan d'image, PSs(x, y) est la fonction d'étalement de point corrigée, et As(x, y) est une amplitude réelle du plan d'image correspondant à la fonction d'étalement de point corrigée ;
    une troisième unité de génération de fonction pupillaire (14) pour générer une troisième fonction pupillaire sur la base de la première amplitude de plan d'image corrigée, dans lequel la troisième unité de génération de fonction pupillaire (14) est configurée pour générer la troisième fonction pupillaire sur la base de l'équation G 2 ξ η = λ 0 f × F 0 − 1 A 2 x y
    Figure imgb0049
    où G2 (ξ, η) est la troisième fonction pupillaire, et F0 -1 [] est un opérateur de transformation inverse pour un opérateur de transformation de Fourier bidimensionnelle F0 [] ; et
    une unité de calcul de front d'onde (15) pour calculer une aberration de front d'onde sur le plan pupillaire sur la base de la troisième fonction pupillaire, dans lequel l'unité de calcul de front d'onde (15) est configurée pour calculer l'aberration de front d'onde sur la base de l'équation W 1 ξ η = 2 π / λ 0 × arg G 2 ξ η
    Figure imgb0050
    où W1(ξ, η) est une fonction représentant l'aberration de front d'onde, et arg[x] est une composante de phase d'un nombre complexe arbitraire x, dans lequel
    l'unité de calcul de front d'onde (15) provoque l'exécution, en entrant les données de l'aberration de front d'onde calculée dans la première unité de génération de fonction pupillaire (11) et la deuxième unité de génération de fonction pupillaire (21), par la première unité de génération de fonction pupillaire (11), la première unité de calcul d'amplitude de plan d'image (12), la deuxième unité de génération de fonction pupillaire (21), la seconde unité de calcul d'amplitude de plan d'image (22), l'unité de correction PSF (23), l'unité d'application de condition de contrainte (13), la troisième unité de génération de fonction pupillaire (14), et l'unité de calcul de front d'onde (15) d'une opération itérative.
  2. Dispositif de calcul de front d'onde selon la revendication 1, dans lequel la première unité de génération de fonction pupillaire (11), la première unité de calcul d'amplitude de plan d'image (12), la deuxième unité de génération de fonction pupillaire (21), la deuxième unité de calcul d'amplitude de plan d'image (22), l'unité de correction PSF (23), l'unité d'application de condition de contrainte (13), la troisième unité de génération de fonction pupillaire (14), et l'unité de calcul de front d'onde (15) exécutent l'opération itérative jusqu'à ce que l'aberration de front d'onde calculée satisfasse une condition de convergence, dans lequel la condition de convergence est une condition selon laquelle une opération itérative est exécutée un nombre de fois préétabli.
  3. Dispositif de calcul de front d'onde selon la revendication 1 ou la revendication 2, comprenant en outre une unité de réglage de front d'onde (10) pour entrer des données d'une aberration de front d'onde initiale définie pour l'opération itérative dans la première unité de génération de fonction pupillaire (11) et la deuxième unité de génération de fonction pupillaire (21).
  4. Dispositif de calcul de front d'onde selon la revendication 1 ou 2, comprenant en outre
    une unité de reconstruction PSF (31) pour reconstruire une seule fonction d'étalement de point sur la base d'une pluralité de fonctions d'étalement de point, dans lequel
    l'unité de reconstruction PSF (31) est configurée pour calculer une phase spatiale de la pluralité de fonctions d'étalement de point et pour reconstruire la fonction d'étalement de point unique en combinant la pluralité de fonctions d'étalement de point sur la base des résultats de calcul, et
    l'unité de reconstruction PSF (31) fournit la fonction d'étalement de point unique comme fonction d'étalement de point mesurée à l'unité de correction PSF (23).
  5. Dispositif de calcul de front d'onde selon la revendication 1 ou la revendication 2, dans lequel la première condition de contrainte est une condition dans laquelle l'intensité sur le plan pupillaire est spatialement limitée.
  6. Dispositif de calcul de front d'onde selon la revendication 1 ou la revendication 2, dans lequel la seconde condition de contrainte est une condition dans laquelle une amplitude réelle de la première amplitude de plan d'image est remplacée par une amplitude réelle d'une amplitude complexe correspondant à la fonction d'étalement de point corrigée par l'unité de correction PSF (23).
  7. Système de mesure de front d'onde comprenant :
    le dispositif de calcul de front d'onde (2A, 2B) selon la revendication 1 ; et
    un détecteur (4A, 4B) pour détecter une ou plusieurs fonctions d'étalement de point en formant une image d'une source lumineuse ponctuelle, dans lequel
    l'unité de correction PSF (23) génère la fonction d'étalement de point mesurée à partir d'une ou plusieurs fonctions d'étalement de point détectées par le détecteur (4A, 4B).
  8. Système de mesure de front d'onde selon la revendication 7, comprenant en outre
    un dispositif de contrôle de front d'onde (5) pour corriger une forme d'un front d'onde de lumière incidente sur la base des données de l'aberration de front d'onde calculée par l'unité de calcul de front d'onde (15) en utilisant un miroir déformable ou en ajustant les caractéristiques optiques d'un système optique de diffraction.
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